Reflected BSDEs and doubly reflected BSDEs driven by RCLL martingales

2021/03/16 by Nie, Tianyang, Rutkowski, Marek
#60H10 #60H30 #91G30 #91G40 #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2103.08917

Abstract

We prove some new results on reflected BSDEs and doubly reflected BSDEs driven by a multi-dimensional RCLL martingale. The goal is to develop a general multi-asset framework encompassing a wide spectrum of nonlinear financial models, including as particular cases the setups studied by Peng and Xu \citePX2009 and Dumitrescu et al. \citeDGQS2018 who dealt with BSDEs driven by a one-dimensional Brownian motion and a purely discontinuous martingale with a single jump. Our results are not covered by existing literature on reflected and doubly reflected BSDEs driven by a Brownian motion and a Poisson random measure.

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